World Football Elo Ratings

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The World Football Elo Ratings is a ranking system for men's national association football teams that is published by the website eloratings.net. It is based on the Elo rating system but includes modifications to take various football-specific variables into account, like the margin of victory, importance of a match, and home field advantage. Other implementations of the Elo rating system are possible and there is no single nor any official Elo ranking for football teams. The FIFA World Rankings -not based on the Elo method- is the official national teams rating system used by the international governing body of football and is therefore more prevalent.

The ratings consider all international "A" matches for which results could be found. Ratings tend to converge on a team's true strength relative to its competitors after about 30 matches.[1] Ratings for teams with fewer than 30 matches should be considered provisional.

The FIFA Women's World Rankings system uses a modified version of the Elo formula whereas the FIFA men's ranking system uses a non-Elo formula. A 2009 comparative study of eight methods found that the implementation of the Elo rating system described below had the highest predictive capability for football matches, while the men's FIFA ranking method performed poorly.[2]

Top 60 ranking[edit]

The following table shows World Football Elo Ratings on 9 September 2016, using data from the World Football Elo Ratings web site.[3]

Each national team's FIFA World Rankings are shown as they were on 15 September 2016.[4]

AFC
CAF
CONCACAF
CONMEBOL
OFC
UEFA

Highest average ratings since 1970[edit]

Time averaged Elo or Elo-like scores are routinely used to compare chess player strengths.[5][6][7] The following is a list of the national teams with the highest average Elo score from 1 January 1970 to 1 September 2016. Before this time intercontinental play was fairly limited and many nations in Africa, North America, and Asia had played too few games yet to create a representative Elo score.

Rank Country Avg Elo
1  Brazil 2015.0
2  Germany[a] 1985.5
3  Netherlands 1929.5
4  England 1926.7
5  Italy 1923.0
6  Spain 1916.4
7  Argentina 1908.7
8  France 1889.8
9  Russia[b] 1851.7
10  Czech Republic[c] 1832.8
11  Portugal 1824.9
12  Serbia[d] 1815.9
13  Sweden 1800.6
14  Romania 1789.1
15  Mexico 1788.0
16  Poland 1777.1
 Uruguay 1777.1
Rank Country Avg Elo
18  Belgium 1771.6
19  Denmark 1769.9
20  Scotland 1741.7
21  Chile 1728.7
22  Paraguay 1726.2
23  Republic of Ireland 1725.0
24  Bulgaria 1705.3
25  Australia 1700.7
27   Switzerland 1696.8
26  Colombia 1695.8
28  Austria 1694.9
29  Hungary 1688.7
30  Iran 1678.0
31  South Korea 1677.3
33  Nigeria 1664.3
32  Greece 1661.3
34  Egypt 1658.5
Rank Country Avg Elo
35  Wales 1658.0
36  Norway 1646.3
37  Peru 1645.5
38  Israel 1643.3
39  Turkey 1643.2
40  Cameroon 1641.8
41  Morocco 1635.0
42  Ivory Coast 1631.8
43  Ghana 1612.1
44  Northern Ireland 1607.9
45  Iraq 1606.2
46  United States 1605.3
47  Tunisia 1598.6
48  Costa Rica 1597.6
49  Japan 1597.5
49  Ecuador 1596.0
51  China PR 1592.5

List of number one teams[edit]

The following is the list of nations who have achieved the number one position in the World Football Elo Ratings since 1872:

Ranking by days as leader[edit]

Nation days First Date as Leader Last Date as Leader
 England 10,295 30 November 1872 11 June 1988
 Argentina 8,815 16 June 1929 Current
 Brazil 8,294 12 June 1958 7 July 2014
 Scotland 5,857 4 March 1876 11 March 1904
 Germany [e] 4,367 25 July 1966 28 May 2016
 Denmark 2,979 2 July 1912 27 August 1920
 Italy 2,673 6 June 1934 15 August 2006
 France 2,597 12 September 1984 10 July 2007
 Spain 2,502 5 September 1920 11 October 2013
 Uruguay 2,281 28 August 1920 8 July 1931
 Hungary 1,694 17 May 1953 11 June 1958
 Russia [f] 1,213 31 March 1963 24 June 1988
 Netherlands 922 29 Aug 1920 3 July 2014
 Austria 11 27 May 1934 6 June 1934
 Czech Republic 8 27 June 2004 7 June 2005

Elo all-time records[edit]

All-time highest ratings[edit]

The following is a list of national football teams ranked by their highest Elo score ever reached. The team in each confederation that has achieved the highest rank is shown in color.

All-time highest ranking[edit]

The following is a list of national football teams ranked by their highest Elo ranking ever reached.

§ In the Elo rankings, the organisation has incorrectly attributed the Ireland national football team prior to 1921 to the association of the Republic of Ireland which was not formed until after 1921. The team continued as Northern Ireland after the Republic of Ireland separated from the United Kingdom.

Averages by decade[edit]

The table below shows the teams with the best average Elo score per decade (Jan 1 19X0 - Dec 31 19X9).

Rank 1920s 1930s 1940s [n] 1950s 1960s
1 1916

 Uruguay

1976

 Argentina

2043

 Argentina

2036

 Argentina

1965

 Brazil

2 1876

 Spain

1970

 Italy

2008

 Italy

2015

 Hungary

1939

 Soviet Union

3 1851

 Argentina

1897

 Uruguay

1891

 England

1996

 Brazil

1928

 Hungary

4 1831

 Scotland

1883

 Austria

1880

 Brazil

1915

 England

1927

 England

5 1822

 Czechoslovakia

1869

 Spain

1861

 Spain

1874

 West Germany

1923

 Argentina

6 1817

 Denmark

1864

 England

1849

 Scotland

1856

 Yugoslavia

1888

 West Germany

7 1783

 Hungary

1843

 Scotland

1846

 Uruguay

1852

 Uruguay

1871

 Czechoslovakia

8 1781

 Brazil

1821

 Czechoslovakia

1839

 Germany

1829

 Austria

1852

 Italy

9 1773

 Austria

1816

 Brazil

1831

 Hungary

1828

 Italy

1844

 Spain

10 1753

 England

1810

 Hungary

1814

 Austria

1808

 Spain

1840

 Uruguay

11 1744

 Netherlands

1769

 Costa Rica

1788

 Czechoslovakia

1803

 Sweden

1825

 Yugoslavia

12 1720

 Sweden

1764

 Germany

1782

 Mexico

1798

 Paraguay

1802

 Scotland

13 1703

 Belgium

1691

 Denmark

1751

 Sweden

1796

 Scotland

1791

 Sweden

14 1695

 Italy

1683

 Sweden

1741

 Wales

1753

 France

1779

 Mexico

15 1678

 Portugal

1677

 Paraguay

1719

 Paraguay

1728

 Czechoslovakia

1737

 Austria

Rank 1970s 1980s 1990s 2000s 2010s [o]
1 2065

 Brazil

1977

 Brazil

2002

 Brazil

1998

 Brazil

2056

 Spain

2 2043

 West Germany

1969

 West Germany

1995

 Germany

1988

 France

2047

 Germany

3 1952

 England

1951

 Soviet Union

1959

 Italy

1970

 Netherlands

2044

 Brazil

4 1930

 Italy

1933

 England

1936

 France

1964

 Argentina

2002

 Netherlands

5 1887

 Netherlands

1897

 Argentina

1926

 Netherlands

1958

 Spain

1977

 Argentina

6 1882

 Poland

1895

 Italy

1909

 Spain

1945

 Italy

1919

 England

7 1876

 Soviet Union

1890

 France

1907

 FR Yugoslavia[p]

1921

 England

1889

 Chile

8 1869

 East Germany

1887

 Netherlands

1906

 England

1895

 Germany

1883

 Portugal

9 1862

 Argentina

1853

 Spain

1878

 Denmark

1890

 Portugal

1883

 Uruguay

10 1853

 Spain

1852

 Poland

1868

 Argentina

1881

 Czech Republic

1868

 Italy

11 1841

 Czechoslovakia

1827

 Belgium

1849

 Czech Republic[q]

1843

 Denmark

1865

 France

12 1836

 Hungary

1825

 East Germany

1842

 Russia[r]

1840

 Croatia

1860

 Colombia

13 1834

 Yugoslavia

1825

 Yugoslavia

1841

 Sweden

1823

 Mexico

1854

 Mexico

14 1815

 Scotland

1824

 Czechoslovakia

1831

 Romania

1810

 Sweden

1836

 Croatia

15 1808

 Portugal

1789

 Scotland

1829

 Croatia

1807

 Romania

1799

 Sweden

16 1794

 Belgium

1788

 Uruguay

1825

 Mexico

1792

 United States

1795

 Russia

17 1780

 Romania

1787

 Romania

1811

 Portugal

1790

 Turkey

1787

 Ecuador

18 1774

 Sweden

1786

 Denmark

1786

 Colombia

1788

 Republic of Ireland

1772

 Ivory Coast

19 1769

 Austria

1780

 Austria

1784

 Norway

1777

 Uruguay

1771

 Switzerland

20 1762

 France

1779

 Sweden

1784

 Republic of Ireland

1775

 Australia

1768

 Ukraine

Highest rated matches[edit]

A list of the 16 matches between teams with the highest combined Elo ratings (the nations' points before the matches are given).

Rank Combined
points
Nation 1 Elo 1 Nation 2 Elo 2 Score Date Occasion Location
1 4242  Germany 2181  Argentina 2061 1 : 0 aet 2014-07-13 World Cup F Brazil Rio de Janeiro
 Germany 2201  Argentina 2041 2 : 4 2014-09-03 Friendly[9] Germany Düsseldorf
3 4219  Netherlands 2104  Spain 2115 0 : 1 aet 2010-07-11 World Cup F South Africa Johannesburg
4 4200  Brazil 2101  Germany 2099 1 : 7 2014-07-08 World Cup SF Brazil Belo Horizonte
5 4195  Brazil 2065  Spain 2130 3 : 0 2013-06-30 Confederations Cup F Brazil Rio de Janeiro
6 4191  West Germany 2002  Hungary 2189 3 : 2 1954-07-04 World Cup F Switzerland Bern
7 4161  Netherlands 2054  Brazil 2107 2 : 1 2010-07-02 World Cup QF South Africa Port Elizabeth
8 4156  West Germany 2071  Brazil 2085 0 : 1 1973-06-16 Friendly West Germany Berlin
9 4153  Brazil 2061  Netherlands 2093 0 : 0 2011-06-04 Friendly Brazil Goiânia
10 4145  Hungary 2138  Brazil 2007 4 : 2 1954-06-27 World Cup QF Switzerland Bern
11 4141  Hungary 2167  Uruguay 1974 4 : 2 1954-06-30 World Cup SF Switzerland Lausanne
12 4136  Netherlands 2076  Argentina 2060 0 : 0 2014-07-09 World Cup SF Brazil São Paulo
12 4136  Spain 2089  Germany 2047 1 : 0 2010-07-07 World Cup SF South Africa Durban
14 4124  Brazil 2054  West Germany 2070 1 : 0 1982-03-21 Friendly Brazil Rio de Janeiro
15 4115  West Germany 2082  Netherlands 2033 2 : 1 1974-07-07 World Cup F West Germany Munich
16 4114  Argentina 2098  Chile 2016 0 : 0 2016-06-26 Copa América F United States East Rutherford

Biggest upsets[edit]

A list of the matches with the biggest point exchange. Since the importance of the match, the goal differential and the perceived home team advantage are factored in the point exchange, these are not necessarily the most surprising wins as expressed by the difference in Elo rating.[s]
The nations' points before the matches are given.

Rank Point
exchange
Nation 1 Elo 1 Nation 2 Elo 2 Score Date Occasion Location
1 93  Sweden 1638  Belgium 1774 8 : 1 1924-05-29 Olympic Games France Paris
2 88  Italy 1769  Spain * 1910 3 : 0 1928-06-04 Olympic Games Netherlands Amsterdam
3 84  Czechoslovakia 1814  Argentina 1964 6 : 1 1958-06-15 World Cup Sweden Helsingborg
4 82  Brazil 2101  Germany 2099 1 : 7 2014-07-08 World Cup Brazil Belo Horizonte
 Fiji 1191  New Zealand 1530 4 : 0 1980-02-23 OFC Nations Cup New Caledonia Nouméa
6 81  Ghana 1599  Czech Republic 1979 2 : 0 2006-06-17 World Cup Germany Cologne
7 80  Egypt * 1619  Hungary 1824 3 : 0 1924-05-29 Olympic Games France Paris
8 78  Croatia 1875  Germany 2060 3 : 0 1998-07-04 World Cup France Lyon
 Khmer Republic 1231  Kuwait 1510 4 : 0 1972-05-14 Asian Cup Thailand Bangkok
 Paraguay 1596  Uruguay 1986 3 : 0 1929-11-01 Copa América Argentina Buenos Aires
11 76  Netherlands 1965  Spain 2089 5 : 1 2014-06-13 World Cup Brazil Salvador
 United States 1866  Mexico 1767 0 : 5 2009-07-26 CONCACAF Gold Cup United States East Rutherford
 Uruguay 1787  Brazil 2122 3 : 0 1959-12-12 Copa América Ecuador Guayaquil
 Chile 1558  Uruguay 1889 3 : 0 1937-01-10 Copa América Argentina Buenos Aires
15 75  Denmark 1724  Italy 1997 5 : 3 1948-08-05 Olympic Games United Kingdom London
 Costa Rica 1684  Guatemala * 1469 1 : 4 1946-03-10 CCCF Championship Costa Rica San José

*The national teams of Spain, Egypt and Guatemala had only played 27, 3, and 25 international matches before their respect upsets, and their Elo rating may still be partially determined by the starting rating they have been assigned (the points exchanges could be lower when these are adjusted).

History[edit]

The Elo system, developed by Hungarian-American mathematician Dr. Árpád Élő, is used by FIDE, the international chess federation, to rate chess players, and by the European Go Federation, to rate Go players. In 1997 Bob Runyan adapted the Elo rating system to international football and posted the results on the Internet. He was also the first maintainer of the World Football Elo Ratings web site, now maintained by Kirill Bulygin.

Overview[edit]

The Elo system was adapted for football by adding a weighting for the kind of match, an adjustment for the home team advantage, and an adjustment for goal difference in the match result.

The factors taken into consideration when calculating a team's new rating are:

  • The team's old rating
  • The considered weight of the tournament
  • The goal difference of the match
  • The result of the match
  • The expected result of the match

The different weights of competitions in descending order are:

These ratings take into account all international "A" matches for which results could be found. Ratings tend to converge on a team's true strength relative to its competitors after about 30 matches. Ratings for teams with fewer than 30 matches should be considered provisional.

Basic calculation principles[edit]

The basic principle behind the Elo ratings is only in its simplest form similar to that of a league, unlike the FIFA tables who effectively run their table as a normal league table, but with weightings to take into account the other factors, the Elo system has its one formula which takes into account the factors mentioned above. There is no first step as in the FIFA system where a team immediately receives points for the result, there is just one calculation in the Elo system.

The ratings change are based on the following formulae:

or

Where;

= The new team rating
= The old team rating
= Weight index regarding the tournament of the match
= A number from the index of goal differences
= The result of the match
= The expected result
= Points Change

The number of Points Change is rounded to the nearest integer before updating the team rating.

Status of match[edit]

The status of the match is incorporated by the use of a weight constant. The weight is a constant regarding the "weight" or importance of a match, defined by which tournament the match is in, they are as follows;

Tournament or Match type Index (K)
World Cup 60
Continental Championship and Intercontinental Tournaments 50
World Cup and Continental qualifiers and major tournaments 40
All other tournaments 30
Friendly Matches 20

Number of goals[edit]

The number of goals is taken into account by use of a goal difference index.

If the game is a draw or is won by one goal

If the game is won by two goals

If the game is won by three or more goals

  • Where N is the goal difference

Table of examples:

Goal Difference Coefficient of K (G)
0 1
+1 1
+2 1.5
+3 1.75
+4 1.875
+5 2
+6 2.125
+7 2.25
+8 2.375
+9 2.5
+10 2.625

Result of match[edit]

W is the result of the game (1 for a win, 0.5 for a draw, and 0 for a loss). This also holds when a game is won or lost on extra time. If the match is decided on penalties, however, the result of the game is considered a draw (W = 0.5).

Expected result of match[edit]

We is the expected result (win expectancy with a draw counting as 0.5) from the following formula:

where dr equals the difference in ratings (add 100 points for the home team). So dr of 0 gives 0.5, of 120 gives 0.666 to the higher-ranked team and 0.334 to the lower, and of 800 gives 0.99 to the higher-ranked team and 0.01 to the lower.

Examples[edit]

The same examples have been used on the FIFA World Rankings for a fair comparison. Some actual examples should help to make the methods of calculation clear. In this instance it is assumed that three teams of different strengths are involved in a small friendly tournament on neutral territory.

Before the tournament the three teams have the following point totals.

Team Points
A 630
B 500
C 480

Thus, team A is by some distance the highest ranked of the three: The following table shows the points allocations based on three possible outcomes of the match between the strongest team A, and the somewhat weaker team B:

Example 1[edit]

Team A versus Team B (Team A stronger than Team B)

Team A Team B Team A Team B Team A Team B
Score 3 : 1 1 : 3 2 : 2
20 20 20 20 20 20
1.5 1.5 1.5 1.5 1 1
1 0 0 1 0.5 0.5
0.679 0.321 0.679 0.321 0.679 0.321
Total (P) +9.63 -9.63 -20.37 +20.37 -3.58 +3.58

Example 2[edit]

Team B versus Team C (both teams approximately the same strength)

When the difference in strength between the two teams is less, so also will be the difference in points allocation. The following table illustrates how the points would be divided following the same results as above, but with two roughly equally ranked teams, B and C, being involved:

Team B Team C Team B Team C Team B Team C
Score 3 : 1 1 : 3 2 : 2
20 20 20 20 20 20
1.5 1.5 1.5 1.5 1 1
1 0 0 1 0.5 0.5
0.529 0.471 0.529 0.471 0.529 0.471
Total (P) +14.13 -14.13 -15.87 +15.87 -0.58 +0.58

Note that Team B loses more ranking points by losing to Team C than by losing to Team A.

See also[edit]

Notes[edit]

  1. ^ Representing West Germany from 1949 to 1990
  2. ^ Combined record of the USSR (1970-1992), the CIS (1992), and Russia national football teams (1992-present)
  3. ^ Combined record of the Czechoslovakian (1970-1992) and Czech national football teams (1993-present)
  4. ^ Combined record of Yugoslavia (1970-1992), Serbia and Montenegro (1994-2006) and Serbia national football teams (2006-present)
  5. ^ Combined record of the Germany (1908-1950 & 1990-present) and West Germany (1950-1990) national football teams.
  6. ^ Combined record of the Russian Empire (1912-1914), RSFSR (1923), USSR (1924-1992), CIS (1992), and Russia (1992-present) national football teams.[8]
  7. ^ as Soviet Union
  8. ^ as FR of Yugoslavia
  9. ^ On 1 January 2006, Football Federation Australia moved from the OFC to the AFC
  10. ^ as Zaire
  11. ^ as Soviet Union
  12. ^ as FR of Yugoslavia
  13. ^ as Zaire
  14. ^ In the 1940s, most national teams did not play games until after the end of World War II, making comparison of countries for this decade weak. For example, Mexico did not play any matches between Feb 1938 and July 1947, so that the average over the decade mostly reflects the single Elo rating achieved in February 1938
  15. ^ up to 1 September 2016
  16. ^ Combined record of Yugoslavia (1990-1992) and FR of Yugoslavia (1994-1999)
  17. ^ Combined record of Czechoslovakia (1990-1992) and Czech national football teams (1993-1999)
  18. ^ Combined record of the USSR (1990-1992), the CIS (1992), and Russia national football teams (1992-1999)
  19. ^ In those terms, most surprising may have been the 2:1 win of Luxembourg (Elo rating 1049) over Switzerland (ER 1730) in a World Cup qualification match in September 2008 (a 681 point difference). In another World Cup qualifier in October 2004 Liechtenstein (ER 1046) held the 810 points higher rated Portuguese team (ER 1856) to a 2:2 draw.

References[edit]

  1. ^ "The World Football Elo Rating System". Eloratings.net. Retrieved 26 February 2012. 
  2. ^ J. Lasek, Z. Szlávik and S. Bhulai (2013), The predictive power of ranking systems in association football, Int. J. Applied Pattern Recognition1: 27-46.
  3. ^ World Football Elo Ratings Eloratings.net. Retrieved: 2016-09-06.
  4. ^ "FIFA/Coca-Cola World Ranking" (Press release). FIFA. 15 September 2016. Retrieved 2016-09-15. 
  5. ^ Arpad E. Elo, The Rating of Chessplayers, Past and Present, Arco, 1978. ISBN 0-668-04721-6.
  6. ^ Arpad Elo, Chess Life, 1962.
  7. ^ About the Chessmetrics Rating System, by Jeff Sonas
  8. ^ "History of the Football Union of Russia". Rfs.ru. Retrieved 2016-06-04. 
  9. ^ "Germany to play Argentina in September friendly". The Star. 21 March 2014. Retrieved 15 July 2014. 

External links[edit]